Quantization is a non-linear operation of converting a continuous
signal into a discrete one, assuming a finite number of levels N. A
study is made of the quantization procedure, starting from the year
1898 to the present time. Conditions for minimum error are derived
with consideration of quantization in magnitude and time. An extension
of the Mehler and Carlitz formulas involving Hermitian polynomials
(quadrilinear case) has been created. Further, investigation is conducted
toward obtaining an autocorrelation function of the output of
the quantizer for Gaussian input. The method calls for the use of two
different forms of the Euler-Maclaurin sum formulas and results are derived
for a hard limiter, linear detector, clipper, and a smooth limiter.
The method lends itself to the extension to the non-uniform case
